A modified beam model based on Gurtin–Murdoch surface elasticity theory

In this work, a modified surface-effect incorporated beam model based on Gurtin and Murdoch (GM) surface elasticity theory is established by satisfying the required balance equations on surfaces, which is often overlooked by researchers in this field. With the refinement, the proposed model is more rigorous in mathematics and mechanics compared with GM theory-based beam models in literature. To demonstrate the model, the problem for static bending of simply supported beam considering surface effects is solved by applying the general equations derived, and numerical results are obtained and discussed.